Discovering the underlying Directed Acyclic Graph (DAG) from time series observational data is highly challenging due to the dynamic nature and complex nonlinear interactions between variables. Existing methods typically search for the optimal DAG by optimizing an objective function but face scalability challenges, as their computational demands grow exponentially with the dimensional expansion of variables. To this end, we propose LOCAL, a highly efficient, easy-to-implement, and constraint-free method for recovering dynamic causal structures. LOCAL is the first attempt to formulate a quasi-maximum likelihood-based score function for learning the dynamic DAG equivalent to the ground truth. Building on this, we introduce two adaptive modules that enhance the algebraic characterization of acyclicity: Asymptotic Causal Mask Learning (ACML) and Dynamic Graph Parameter Learning (DGPL). ACML constructs causal masks using learnable priority vectors and the Gumbel-Sigmoid function, ensuring DAG formation while optimizing computational efficiency. DGPL transforms causal learning into decomposed matrix products, capturing dynamic causal structure in high-dimensional data and improving interpretability. Extensive experiments on synthetic and real-world datasets demonstrate that LOCAL significantly outperforms existing methods and highlight LOCAL's potential as a robust and efficient method for dynamic causal discovery.

翻译：从时间序列观测数据中发现潜在的有向无环图（DAG）极具挑战性，这源于变量的动态特性及变量间复杂的非线性相互作用。现有方法通常通过优化目标函数来搜索最优DAG，但面临可扩展性挑战，因为其计算需求随变量维度的扩展呈指数级增长。为此，我们提出LOCAL，一种高效、易于实现且无约束的动态因果结构恢复方法。LOCAL首次尝试构建一个基于拟极大似然的评分函数，用于学习与真实因果图等价的动态DAG。在此基础上，我们引入了两个增强无环性代数表征的自适应模块：渐近因果掩码学习（ACML）与动态图参数学习（DGPL）。ACML利用可学习的优先级向量和Gumbel-Sigmoid函数构建因果掩码，在优化计算效率的同时确保DAG的形成。DGPL将因果学习转化为分解的矩阵乘积，以捕捉高维数据中的动态因果结构并提升可解释性。在合成数据集和真实数据集上进行的大量实验表明，LOCAL显著优于现有方法，并凸显了其作为动态因果发现的鲁棒高效方法的潜力。